editing disabled

The temperaments listed are 53edo-distinct, meaning that they are all different even if tuned in 53edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -15]]
Helmholtz
3.103
32805/32768
2
<<2 37 54]]
Monzismic
12.528
|54 -37 2>
3
<<3 29 39]]
Tricot
9.520
68719476736000/68630377364883
4
<<4 21 24]]
Vulture
6.600
10485760000/10460353203
5
<<5 13 9]]
Amity
3.970
1600000/1594323
6
<<6 5 -6]]
Hanson
2.685
15625/15552
7
<<7 -3 -21]]
Orson
4.232
2109375/2097152
8
<<8 -11 -36]]
Submajor
6.919
69198046875/68719476736
9
<<9 -19 -51]]
Aufo
9.853
2270041927734375/2251799813685248
10
<<10 -27 -66]]

12.867
74468725439326171875/73786976294838206464
11
<<11 18 3]]
Quartonic
6.026
390625000/387420489
12
<<41 43 -27]]

18.85
|-27 -43 41>
13
<<13 2 -27]]
Ditonic
6.373
1220703125/1207959552
14
<<14 47 42]]

14.353
|42 -47 14>
15
<<15 -14 -57]]
Misneb
11.043
145964630126953125/144115188075855872
16
<<16 31 12]]

9.845
625000000000000/617673396283947
17
<<17 23 -3]]
Maja
8.443
762939453125/753145430616
18
<<35 38 -21]]

16.207
|-21 -38 35>
19
<<19 7 -33]]
Semaja
8.817
19073486328125/18786186952704
20
<<20 -1 -48]]

10.481
286102294921875/281474976710656
21
<<21 44 21]]

13.75
1000000000000000000000/984770902183611232881
22
<<31 17 -45]]

13.972
4656612873077392578125/4543715546604414959616
23
<<23 28 -9]]

10.985
11920928955078125/11712917736940032
24
<<29 33 -15]]

13.582
186264514923095703125/182159296644891377664
25
<<25 12 -39]]

11.37
298023223876953125/292162779488452608
26
<<27 -4 -69]]

14.659
603497028350830078125/590295810358705651712

7-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -14 -15 -25 -10]]
Garibaldi
3.823
225/224 3125/3087
2
<<2 -16 25 -30 34 103]]
Hemischis
9.155
6144/6125 19683/19600
3
<<3 29 11 39 9 -56]]
Tricot
7.801
2430/2401 5120/5103
4
<<4 21 -3 24 -16 -66]]
Buzzard
6.420
1728/1715 5120/5103
5
<<5 13 -17 9 -41 -76]]
Amity
7.127
4375/4374 5120/5103
6
<<6 5 22 -6 18 37]]
Catakleismic
4.684
225/224 4375/4374
7
<<7 -3 8 -21 -7 27]]
Orwell
3.685
225/224 1728/1715
8
<<8 -11 -6 -36 -32 17]]
Submajor
5.869
225/224 51200/50421
9
<<9 -19 -20 -51 -57 7]]
Untriton
9.195
225/224 125000000/121060821
10
<<10 26 19 18 2 -29]]
Hamity
6.518
2430/2401 4000/3969
11
<<11 18 5 3 -23 -39]]
Quartonic
5.395
1728/1715 4000/3969
12
<<12 10 -9 -12 -48 -49]]
Hemikleismic
6.704
4000/3969 6144/6125
13
<<13 2 30 -27 11 64]]
Coditone
7.512
225/224 2125764/2100875
14
<<14 47 16 42 -14 -95]]

12.061
19683/19600 51200/50421
15
<<15 -14 2 -57 -39 44]]
Misneb
9.025
225/224 4194304/4117715
16
<<16 31 41 12 20 8]]

9.361
3125/3087 19683/19600
17
<<17 23 27 -3 -5 -2]]
Maja
7.161
2430/2401 3125/3087
18
<<18 15 13 -18 -30 -12]]
Kleiboh
6.645
1728/1715 3125/3087
19
<<19 7 -1 -33 -55 -22]]
Semaja
8.139
3125/3087 6144/6125
20
<<20 -1 -15 -48 -80 -32]]

10.843
3125/3087 65536/64827
21
<<21 44 24 21 -21 -68]]

11.339
4000/3969 839808/823543
22
<<31 17 43 -45 -19 52]]

12.262
2430/2401 390625/387072
23
<<23 28 49 -9 13 35]]

10.832
4375/4374 78125/76832
24
<<24 20 35 -24 -12 25]]

9.340
2430/2401 15625/15552
25
<<25 12 21 -39 -37 15]]

9.293
1728/1715 78125/76832
26
<<26 4 7 -54 -62 5]]

10.711
6144/6125 78125/76832

11-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -14 -30 -15 -25 -51 -10 -42 -36]]
Helenus
5.390
99/98 176/175 3125/3087
2
<<2 -16 -28 -7 -30 -50 -18 -20 39 77]]
Hemigari
6.723
121/120 225/224 3125/3087
3
<<3 29 11 16 39 9 15 -56 -63 7]]
Tricot
6.753
99/98 121/120 5120/5103
4
<<4 21 -3 -14 24 -16 -36 -66 -105 -29]]
Buteo
6.975
99/98 385/384 2200/2187
5
<<5 13 -17 9 9 -41 -3 -76 -24 84]]
Hitchcock
6.290
121/120 176/175 2200/2187
6
<<6 5 22 32 -6 18 30 37 57 14]]
Cataclysmic
5.473
99/98 176/175 2200/2187
7
<<7 -3 8 2 -21 -7 -21 27 15 -22]]
Orwell
3.242
99/98 121/120 176/175
8
<<8 -11 -6 -28 -36 -32 -72 17 -27 -58]]
Interpental
7.011
99/98 176/175 51200/50421
9
<<9 -19 -20 -5 -51 -57 -39 7 54 55]]
Untriton
7.983
121/120 225/224 22000/21609
10
<<10 26 19 18 18 2 -6 -29 -48 -15]]
Hamity
5.668
99/98 121/120 4000/3969
11
<<11 18 5 -12 3 -23 -57 -39 -90 -51]]
Quartz
6.692
99/98 385/384 4000/3969
12
<<12 10 -9 11 -12 -48 -24 -49 -9 62]]
Hemikleismic
5.839
121/120 176/175 4000/3969
13
<<13 2 30 34 -27 11 9 64 72 -8]]
Coditone
7.203
99/98 176/175 6655/6561
14
<<14 -6 -37 4 -42 -98 -42 -69 30 139]]

11.245
121/120 4000/3969 4125/4096
15
<<15 -14 2 27 -57 -39 -9 44 111 69]]
Musneb
8.909
225/224 385/384 66550/64827
16
<<16 31 41 50 12 20 24 8 9 -1]]

8.690
99/98 2662/2625 3125/3087
17
<<17 23 27 20 -3 -5 -27 -2 -33 -37]]
Maja
6.299
99/98 121/120 3125/3087
18
<<18 15 13 43 -18 -30 6 -12 48 76]]
Kleiboh
7.194
176/175 540/539 3125/3087
19
<<19 7 -1 13 -33 -55 -45 -22 6 40]]
Semaja
7.046
121/120 176/175 3125/3087
20
<<20 -1 38 36 -48 4 -12 91 87 -30]]

9.738
99/98 176/175 161051/157464
21
<<21 44 24 6 21 -21 -63 -68 -138 -66]]

11.170
99/98 4000/3969 9317/9216
22
<<22 36 10 29 6 -46 -30 -78 -57 47]]

9.340
121/120 1728/1715 4000/3969
23
<<23 28 49 52 -9 13 3 35 24 -23]]

9.720
99/98 2662/2625 4375/4374
24
<<24 20 35 22 -24 -12 -48 25 -18 -59]]

8.261
99/98 121/120 78125/76832
25
<<25 12 21 45 -39 -37 -15 15 63 54]]

8.873
176/175 540/539 66550/64827
26
<<26 4 7 15 -54 -62 -66 5 21 18]]

9.286
121/120 176/175 34375/33614

13-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -14 -30 -33 -15 -25 -51 -56 -10 -42 -47 -36 -41 -3]]
Helenus
5.812
99/98 176/175 275/273 847/845
2
<<2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19]]
Hemigari
6.013
121/120 169/168 225/224 275/273
3
<<3 29 11 16 7 39 9 15 0 -56 -63 -91 7 -21 -35]]
Tricot
6.236
99/98 121/120 169/168 352/351
4
<<4 21 -3 -14 27 24 -16 -36 28 -66 -105 -15 -29 87 145]]
Buteo
7.137
99/98 275/273 385/384 572/567
5
<<5 13 -17 9 -6 9 -41 -3 -28 -76 -24 -62 84 46 -54]]
Hitchcock
5.834
121/120 169/168 176/175 325/324
6
<<6 5 22 32 14 -6 18 30 0 37 57 14 14 -42 -70]]
Cataclysmic
4.918
99/98 169/168 176/175 275/273
7
<<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]]
Orwell
4.717
99/98 121/120 176/175 275/273
8
<<8 -11 -6 25 1 -36 -32 12 -28 17 96 43 91 25 -89]]
Submajor
6.305
169/168 225/224 275/273 385/384
9
<<9 -19 -20 -5 -32 -51 -57 -39 -84 7 54 -4 55 -16 -92]]
Untriton
8.047
121/120 225/224 275/273 1040/1029
10
<<10 26 19 18 41 18 2 -6 28 -29 -48 -1 -15 45 75]]
Hamity
5.887
99/98 121/120 275/273 572/567
11
<<11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72]]
Quartz
5.990
99/98 169/168 275/273 385/384
12
<<12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56]]
Hemikleismic
6.023
121/120 176/175 275/273 325/324
13
<<13 2 30 34 48 -27 11 9 28 64 72 104 -8 24 40]]
Coditone
7.622
99/98 176/175 325/324 847/845
14
<<14 -6 16 4 15 -42 -14 -42 -28 54 30 57 -44 -17 37]]
Doublethink
5.858
99/98 121/120 169/168 176/175
15
<<15 -14 2 -26 -18 -57 -39 -93 -84 44 -12 10 -80 -58 34]]
Misneb
8.837
99/98 176/175 640/637 847/845
16
<<16 -22 -12 -3 2 -72 -64 -60 -56 34 69 86 33 50 18]]

9.127
121/120 169/168 225/224 640/637
17
<<17 23 27 20 22 -3 -5 -27 -28 -2 -33 -34 -37 -38 2]]
Maja
5.680
99/98 121/120 169/168 275/273
18
<<18 15 13 43 42 -18 -30 6 0 -12 48 42 76 70 -14]]
Kleiboh
6.913
176/175 275/273 325/324 540/539
19
<<19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]]
Semaja
6.343
121/120 169/168 176/175 275/273
20
<<20 -1 38 36 29 -48 4 -12 -28 91 87 71 -30 -59 -33]]

8.717
99/98 169/168 176/175 4235/4212
21
<<21 -9 24 6 -4 -63 -21 -63 -84 81 45 24 -66 -100 -36]]

9.168
99/98 121/120 176/175 2200/2197
22
<<22 36 10 29 16 6 -46 -30 -56 -78 -57 -96 47 8 -52]]

8.657
121/120 169/168 325/324 640/637
23
<<23 28 49 52 36 -9 13 3 -28 35 24 -20 -23 -80 -68]]

8.776
99/98 169/168 275/273 2662/2625
24
<<24 20 35 22 3 -24 -12 -48 -84 25 -18 -67 -59 -121 -71]]

8.623
99/98 121/120 275/273 4225/4224
25
<<25 12 21 45 23 -39 -37 -15 -56 15 63 9 54 -13 -87]]

8.025
169/168 176/175 275/273 540/539
26
<<26 4 7 15 43 -54 -62 -66 -28 5 21 85 18 95 93]]

9.145
121/120 176/175 676/675 1040/1029